The PROBLEM Solver is an open source Python implementation of the proton radiography reconstruction algorithm of Bott et al. (2017) 1. The project currently includes two example problems to demonstrate the algorithm. When completed, it will provide tools to support reconstruction of magnetic fields from simulated and experimental proton radiography data for high-energy laser experiments.
Proton radiography is an invaluable tool for gathering information about the strength and topology of magnetic fields in high-energy laser plasma experiments (Li et al. 2006). The diagnostic utilizes high-energy protons that travel through a magnetized plasma and whose paths are altered by the magnetic fields present in the plasma. After the interaction, the protons propagate to a screen where they impart an image, thereby recording information about magnetic field deflections. The image can then be analyzed after the experiment to understand the structure of the magnetic field inside the plasma.
If the magnetic field strength is small enough in a plasma, the proton paths remain injective during proton radiography. In this case, it can be shown that the path-integrated magnetic field may be reconstructed from the proton image (Graziani et al. 2016; Bott et al. 2017). In proton radiography, after the protons travel through the magnetic field, the information regarding their deflections is imparted in the flux image. We would like to transform the proton flux image back into information regarding the proton deflections.
In Bott et al. (2017), it is shown that reconstructing the magnetic field from a proton image is equivalent to solving the following logarithmic parbolic Monge-Ampère equation for the steady state solution of Φ:
PROBLEM transforms proton flux data into this Monge-Ampère problem and then implements a solver to reconstruct the path-integrated magnetic field.
Requirements:
The requirements may be installed according to the directions on
their webpages, or with any Python
package manager that supports them. For example, one could use pip to install
them as
pip install numpy scipy matplotlibOne could also use Anaconda Python to install them as
conda install numpy scipy matplotlibAfter installing the required packages, we may install PROBLEM as
git clone https://github.com/flash-center/PROBLEM.git
cd PROBLEM/
python setup.py installThe donut is an ellipsoidal blob of magnetic field,
To run this example problem,
cd ~/PROBLEM/examples/donut/
problem-solver input.txt --xstep .001 --ystep .001Note: the input.txt file was generated by the
PRadReader package by calling
pradreader flux.datand entering the relevant information at the prompts (located in README.txt).
Checkpoint files for every 1000 steps will be saved in the solve/ directory.
Now, we run our script to plot the magnetic field strength at each step,
python plot_images.pyThis script will save the image of the magnetic field at each time step to the
images/ directory for viewing.
The strip is an vertical strip of magnetic field, designed to test the boundaries of the PROBLEM solver,
To run this example problem,
cd ~/PROBLEM/examples/strip/
problem-solver input.txt --xstep .0005 --ystep .0005Note: the input.txt file was generated by the
PRadReader package by calling
pradreader flux.datand entering the relevant information at the prompts (located in README.txt).
Checkpoint files for every 1000 steps will be saved in the solve/ directory.
Now, we run our script to plot the magnetic field strength at each step,
python plot_images.pyThis script will save the image of the magnetic field at each time step to the
images/ directory for viewing.